{
  "id": "1501.04873",
  "version": "v1",
  "published": "2015-01-20T16:37:45.000Z",
  "updated": "2015-01-20T16:37:45.000Z",
  "title": "Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem",
  "authors": [
    "Simao P. S. Santos",
    "Natalia Martins",
    "Delfim F. M. Torres"
  ],
  "comment": "This is a preprint of a paper whose final and definite form will be published in the journal Discrete and Continuous Dynamical Systems. Series A, ISSN 1078-0947 (Print), ISSN 1553-5231 (Online). Submitted 01/May/2014; revised 14/Oct/2014; accepted for publication 20/Jan/2015",
  "categories": [
    "math.OC"
  ],
  "abstract": "We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the first Noether theorem for variational problems with time delay recently proved in [Numer. Algebra Control Optim. 2 (2012), no. 3, 619-630]. Our main result is also a generalization of the first Noether-type theorem for the generalized variational principle of Herglotz proved in [Topol. Methods Nonlinear Anal. 20 (2002), no. 2, 261-273].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-20T16:37:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K15",
      "49S05",
      "34H05"
    ],
    "keywords": [
      "noethers first theorem",
      "variational problems",
      "time delay",
      "herglotz type",
      "dubois-reymond necessary optimality condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104873S"
    }
  }
}